The present invention relates, in general, to microelectromechanical (MEM) structures, and particularly to sensors, filters, switches and the like which utilize variable capacitors for driving and for measuring displacement, as well as to circuitry for measuring output signals produced by such capacitors and for producing drive signals at frequencies selected to produce parametric resonances having sharp transitions between stable and unstable motion of MEM structures.
The generic term xe2x80x9cmicroelectromechanical systemxe2x80x9d (or MEMS) has been applied to the broad field of micromachining and refers to structures such microsensors, microactuators, microinstruments, microoptics, and microfluidics. The applications of these devices are wide-ranging and include accelerometers, which may be used, for example, to deploy automobile airbags, inkjet printer heads and other fluidic devices, arrays of movable mirrors for color projection displays, atomic probes for imaging and transporting atoms, and the like. MEMS devices typically use silicon as a structural material, with the devices being fabricated using integrated circuit technology and more particularly using the single crystal reactive etch and metalization (SCREAM) process which is described, for example, in U.S. Pat. No. 5,719,073, issued Feb. 17, 1998, the disclosure of which is hereby incorporated herein by reference.
Although the use of MEM systems is becoming widely accepted, these micrometer-scale devices present challenges in the real time measurement of device motion, for such devices exhibit multiple modes of motion, have nonlinearities in their spring constants and damping, and exhibit other deviations from the simple models which are often used to describe the motion of mechanical structures. Precise real-time measurements of these devices are needed to understand, to model, and to control these effects. The measurement of device motion and parameters at the nanometer-scale has been done using microinstrumentation fabricated on the same chip as the test devices through the use of variable capacitor motion sensors. However, the use of variable capacitors to measure motion assumes the capacitor structure is stable throughout the measurement; that is, that the gap remains constant and the capacitor electrodes do not rotate or move in a direction perpendicular to the direction of the desired motion to be measured.
One reason for the difficulty in measurements is that in many resonant microelectromechanical systems with electrostatic actuation, the application of a voltage to the device for driving it or for measuring changes in capacitance, changes the effective stiffness of the system. In certain systems, the application of a periodic voltage causes the stiffness to be changed periodically. The equation of motion for such a system is the Mathieu equation:                               ⅆ          2                ⁢        θ                    ⅆ                  τ          2                      +                  (                  β          +                      2            ⁢                          xe2x80x83                        ⁢            δ            ⁢                          xe2x80x83                        ⁢            cos            ⁢                          xe2x80x83                        ⁢            2            ⁢            τ                          ⁢                  xe2x80x83                )            ⁢      θ        =  0
Mathieu equation has been studied extensively in many physical contexts because it governs the pumping of a swing, the stability of ships and columns, Faraday crispations in surface waves on water, electrons in Penning traps, and parametric amplifiers based on electronic or superconducting devices. Many theoretical studies have been carried out on the Mathieu equation, but most of them have been macroscopic, and in these cases damping limits the obtainable experimental results.
The present invention is directed to MEM structures which may be parametrically driven to provide stable operation and to permit precise switching between stable and unstable operations by very small changes in the drive frequency or by very small changes in the characteristics of the structure itself so as to provide improved control and sensing. Although the techniques of the present invention are applicable to a wide variety of microstructures, including parallel plate linear actuators, reduction and augmentation actuators, and linear force comb actuators, the invention will be described herein in terms of torsional devices, and in particular to torsional scanning probe z-actuators having an integrated tip, such as the device described in the above-mentioned U.S. Pat, No. 6,000,280. This device is a micromechanical torsional resonator which incorporates capacitive actuators, or drivers, for producing mechanical motion, and more particularly is a structure which incorporates an improved comb-type actuator structure which consists of high aspect ratio MEM beams fabricated as interleaved fixed and movable capacitor fingers. The device is fabricated from single-crystal silicon and includes a cantilevered beam connected to an adjacent substrate by a torsion bar, within an atomically sharp tip formed on the beam. The capacitive actuator structure can be used either for sensing displacements or inducing motion, the capacitive plates of the fixed and movable fingers allowing a wide range of motion and high amplitudes without failure. This type of actuator generates out of plane motion forces between the fixed and movable fingers due to a phenomenon known as comb-drive levitation, wherein a voltage is applied to the fixed electrodes on the silicon substrate, while the substrate and the adjacent movable electrodes are grounded. This causes asymmetrical fringing electric fields between the movable and fixed electrodes which induce motion in the movable electrodes. Such a micromechanical torsional resonator obeys the Mathieu equation:
(xcex8xe2x80x3+axcex8xe2x80x2+(xcex2+2xcex4 cos 2xcfx84)xcex8=0
where
a=c/2xcfx89I
xcex2=(k+xcex3ADC)/4xcfx892I
and
xcex4=(xcex3AAC)/4xcfx892I
where I is the mass moment of inertia of the torsional cantilever, c is the torsional damping constant, k is torsional stiffness, and M is the applied torque, xcex3 is a parameter that corresponds to the drive strength, xcfx89 is the driving frequency, and A is the input strength under normal operation.
It has been found that such a MEM resonator exhibits unique stability properties, wherein multiple regions in the xcex2-xcex4 parameter space have unstable solutions so that the resonator exhibits resonance-like behavior under several different conditions. The boundaries between these conditions of instability and regions where stable behavior is exhibited are extremely sharp so that a very small change in the frequency of a drive signal and, the characteristics of the MEM device, or a change in a parameter being measured can switch the vibrational motion of the MEM device from a stable to an unstable condition, or vice versa. It has been found that a to frequency change of as little as 0.001 Hz at 114 kHz in the drive signal can effect this change.
When operating in an instability region, the MEM devices of the invention provide increased sensitivity to changes in measured parameters, such as force measurements in an atomic force microscope (AFM). For example, in conventional atomic force microscopes, a high Q in the sensor device leads to higher sensitivity, but at the expense of bandwidth. By utilizing the parametric resonance instability of the present invention, the effect of Q can be decoupled from sensitivity. Further, since the device has such a high sensitivity to changes in frequency between its stable and unstable vibratory conditions, a small force; i.e., the force to be measured, applied to the MEM device can change its characteristics and cause it to xe2x80x9cjumpxe2x80x9d across the boundary from an unstable to stable condition. Because the boundary is so sharp, very small force interactions can be measured. The forces being measured in such a device manifest themselves as changes in the torsional stiffness k of the device. Thus, a change in k will shift the position of the sharp boundary, changing the state of the resonator from xe2x80x9conxe2x80x9d to xe2x80x9coffxe2x80x9d, or vice versa. In addition, small changes in the voltage or frequency can be used independently to move the operating state from stable to unstable because of the dependence of the parameters xcex2 and xcex4 on these values.
The shape of the instability regions can also be changed by changing the device design. For example, by changing the xcex30 parameter, which is the applied force, the slope of the instability boundary changes, and this can be useful in trying to adjust operating characteristics such as the bandwidth of the stable region. Damping in the system also has an effect, for it xe2x80x9croundsxe2x80x9d the bottom of the instability region and narrows its bandwidth. Thus, by changing the damping, which can be produced, for example, by changing the pressure in the environment of the system, the bandwidth or the lower boundary of the instability region is changed.
It has also been found that the Mathieu behavior of torsional resonators and other MEM devices can also be used to reduce parasitic signals in capacitive sensing. This is done by separating the drive and the sensing signals by parametrically exciting the MEM device at a frequency that is far from its natural resonant frequency. This is made possible in the present MEM systems since they are governed by Mathieu type equations, with the result that energy is transferred during parametric excitation in a unique manner. For example, if a given device with a natural frequency of xcfx890=57 kHz is driven at a frequency xcfx89, where xcfx89 corresponds to the first Mathieu instability, where n=1 then xcfx89 will equal 2xcfx890/n which in this case is equal to 114 kHz. A parasitic signal which is included in the output from the MEM device will also be at a harmonic of the natural frequency; that is, 2xcfx890, which is at 114 kHz in this case. However, the MEM device, when driven at the parametric frequency of 114 kHz will still vibrate torsionally at its natural frequency of 57 kHz, so the capacitive sensing signals of interest will be at 57 kHz. With this separation in frequency, it is straightforward to filter out the parasitic 114 kHz signal, thereby revealing the desired 57 kHz sensing signal.
Parametric resonance also holds promise as a mass sensor, for example in biochemical and medical fields for sensing such things as chemical reactions which result in mass changes. Because of the sharp transition from stability to instability, which depends on device parameters, a resonator provides an extremely sensitive way to measure such things as small changes in the mass of a device. A parametric mass sensor may be, for example, an in-plane, parallel plate capacitive actuator, although various actuator configurations may be used.
In summary, the present invention is directed to a parametric resonance oscillator which comprises a microelectromechanical structure mounted for motion with respect to a substrate, wherein the structure has a natural resonant frequency of oscillation. The structure includes a motion sensor which, in the preferred embodiment, includes capacitive plates on the moving structure and adjacent stationary structure. A drive circuit supplies a drive signal to the electrodes at a frequency which is selected to produce parametric oscillation of the MEM structure. This n=1 parametrically resonant frequency is greater than the natural resonant frequency of the structure and provides a sharp boundary between stable and unstable operation, permitting a switching between these two conditions to improve the sensitivity of measurements made by the structure, and improving the accuracy of capacitive measurements through the elimination of parasitic frequencies.